Once the last ability resolves, it will be in effect for the rest of the game. It doesn't matter if Stigma Lasher remains on the battlefield or not.

If a player has been dealt damage by Stigma Lasher, the following things are true: -- Spells and abilities that would normally cause that player to gain life still resolve, but the life-gain part simply has no effect. -- If a cost includes having that player gain life (like Invigorate's alternative cost does), that cost can't be paid. -- Effects that would replace having that player gain life with some other effect won't be able to do anything because it's impossible for that player to gain life. -- Effects that replace an event with having that player gain life (like Words of Worship's effect does) will end up replacing the event with nothing. -- If an effect says to set that player's life total to a certain number, and that number is higher than the player's current life total, that part of the effect won't do anything. (If the number is lower than that player's current life total, the effect will work as normal.)